Multispecies asymmetric simple exclusion process and its relation to traffic flow

Using the matrix product formalism we formulate a natural p-species general ization of the asymmetric simple exclusion process, using the matrix produc t formalism. In this model particles hop with their own specific rate and f ast particles can overtake slow ones with a rate equal to their relative sp eed. We obtain the algebraic structure and study the properties of the repr esentations in detail. The uncorrelated steady state for the open system is obtained and in the p-->(infinity) limit, the dependence of its characteri stics on the distribution of velocities is determined. It is shown that whe n the total arrival rate of particles exceeds a certain value, the density of the slowest particles rises abruptly. [S1063-651X(99)07501-7].